Penalized likelihood and multi-objective spatial scans for the detection and inference of irregular clusters.

Abstract

Background: Irregularly shape d spatial clusters are difficult to delineate. A cluster found by an algorithm often spreads through large portions of the map, impacting its geographical meaning. Penalized likelihood methods for Kulldorff’ s spatial scan statistics have been used to control the excessive freedom of the shape of clusters . Penalty functions based on cluster geometry and non-connectivity have been proposed recently. Another approach involves the use of a multi objective algorithm to maximize two objectives: the spatial scan statistics and the geometric penalty function. Results & Discussion: We present a novel scan statistic algorithm employing a function based on the graph topology to penalize the presence of under -populated disconnection nodes in candid ate clusters , the disconnection nodes cohesion function. A disconnection node is defined as a region within a cluster, such that its removal disconnects the cluster. By applying this function , the most geographicall y meaning ful clusters are sifted through the immense set of possible irregularly shaped candidate cluster solutions. To evaluate the statistical significance of solutions for multi-objective scans, a statistical approach based on the concept of attainment function is use d. In this pa per we compared different penalized likelihoods employing the geometric and non-connectivity regularity functions and the novel disconnection nodes cohesion function . We also build multi-objective scans using those three functions and compare them with the previous penalized likelihood scans. An application is presented using comprehensive state-wide data for Chagas’ disease in puerperal women in Minas Gerais state, Brazil. Conclusions : We show that, compared to the other single-objective algorithm s, multi- objective scans present better performance, regarding power, sensitivity and positive predicted value. The multi objective non-connectivity scan is faster and better suited for the detect ion of moderately irregularly shaped clusters. The multi-objective cohesion scan is most effective for the detection of highly irregularly shaped clusters .